I'd be willing to even go so far as to make some races have more than one type.The only non-humanoid creature type that you can play so far in 5e is Fey. Centaurs, Satyrs, Hexblood, and now the Fairy. I would love to have other options, like Celestials (Bariaur, anyone?), Fiends (Cambions?), and Aberrations (maybe a Ceremorph lineage, like the Gnome Ceremorphs from Rime of the Frostmaiden).
But, yeah, so far there's only two creature types that you can play, and IMHO it sucks.
Dragonborn could count as both humanoids and dragons, for instance. Warforged could be both humanoid and construct. Tieflings could be both humanoid and fiend, while aasimar could be both humanoid and celestial. And so on.